If rectangle abcd is dilated by a scale factor of 1.5 with a center of dilation at vertex a, how does the area of a'b'c'd' compare with the area of abcd?

A’/A = 2.25

Step-by-step explanation:

Let the length and width of ABCD be l and w respectively.

A = lw

For rectangle A’B’C’D’  

l’ = 1.5l and w’ = 1.5w

A’ = l’w’

A’ = 1.5l × 1.5 w

A’ = 2.25 lw

A’/A = 2.25lw/(lw)     Cancel lw

A’/A = 2.25

The area of the dilated rectangle is 2.25 times that of the original.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

think about it deeply and passionately about this property

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